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<b>QuantLib</b>::<a class="el" href="class_quant_lib_1_1_cashflows.html">Cashflows</a></div>
<h1>Cashflows Class Reference</h1><!-- doxytag: class="QuantLib::Cashflows" --><code>#include <ql/CashFlows/analysis.hpp></code>
<p>
<a href="class_quant_lib_1_1_cashflows-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2>
cashflows analysis functions
<p>
<dl compact><dt><b><a class="el" href="todo.html#_todo000002">Todo:</a></b></dt><dd>add tests </dd></dl>
<p>
<table border="0" cellpadding="0" cellspacing="0">
<tr><td></td></tr>
<tr><td colspan="2"><br><h2>Static Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">static <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_cashflows.html#0787b5a6401d359520d6b74c4250601e">npv</a> (const std::vector< boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_cash_flow.html">CashFlow</a> > > &, const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a>< <a class="el" href="class_quant_lib_1_1_yield_term_structure.html">YieldTermStructure</a> > &)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">NPV of the cash flows. <a href="#0787b5a6401d359520d6b74c4250601e"></a><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">static <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_cashflows.html#cb7212d4823e87c8065e3815a1700c45">npv</a> (const std::vector< boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_cash_flow.html">CashFlow</a> > > &, const <a class="el" href="class_quant_lib_1_1_interest_rate.html">InterestRate</a> &, <a class="el" href="class_quant_lib_1_1_date.html">Date</a> settlementDate=<a class="el" href="class_quant_lib_1_1_date.html">Date</a>())</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">NPV of the cash flows. <a href="#cb7212d4823e87c8065e3815a1700c45"></a><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">static <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_cashflows.html#9275953ec871b533c6f9dbd28028f4d8">bps</a> (const std::vector< boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_cash_flow.html">CashFlow</a> > > &, const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a>< <a class="el" href="class_quant_lib_1_1_yield_term_structure.html">YieldTermStructure</a> > &)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Basis-point sensitivity of the cash flows. <a href="#9275953ec871b533c6f9dbd28028f4d8"></a><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">static <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_cashflows.html#339005671cfd4aa3d655c5a973776ef3">bps</a> (const std::vector< boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_cash_flow.html">CashFlow</a> > > &, const <a class="el" href="class_quant_lib_1_1_interest_rate.html">InterestRate</a> &, <a class="el" href="class_quant_lib_1_1_date.html">Date</a> settlementDate=<a class="el" href="class_quant_lib_1_1_date.html">Date</a>())</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Basis-point sensitivity of the cash flows. <a href="#339005671cfd4aa3d655c5a973776ef3"></a><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">static <a class="el" href="group__types.html#gede435af51236692b1107d7639581d39">Rate</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_cashflows.html#ab6aff01e22a5a1d97ccde47a65a882f">irr</a> (const std::vector< boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_cash_flow.html">CashFlow</a> > > &, <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> marketPrice, const <a class="el" href="class_quant_lib_1_1_day_counter.html">DayCounter</a> &dayCounter, Compounding compounding, <a class="el" href="group__datetime.html#g6d41db8ba0ea90d22df35889df452ada">Frequency</a> frequency=NoFrequency, <a class="el" href="class_quant_lib_1_1_date.html">Date</a> settlementDate=<a class="el" href="class_quant_lib_1_1_date.html">Date</a>(), <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> tolerance=1.0e-10, Size maxIterations=10000, Rate guess=0.05)</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Internal rate of return. <a href="#ab6aff01e22a5a1d97ccde47a65a882f"></a><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">static <a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_cashflows.html#4758e38bc3be6c9b70d36f8b6ca5dbdc">duration</a> (const std::vector< boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_cash_flow.html">CashFlow</a> > > &, const <a class="el" href="class_quant_lib_1_1_interest_rate.html">InterestRate</a> &y, Duration::Type type=Duration::Modified, <a class="el" href="class_quant_lib_1_1_date.html">Date</a> settlementDate=<a class="el" href="class_quant_lib_1_1_date.html">Date</a>())</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Cash-flow duration. <a href="#4758e38bc3be6c9b70d36f8b6ca5dbdc"></a><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">static <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="class_quant_lib_1_1_cashflows.html#0a537cb39484e47843ee6da7e5320754">convexity</a> (const std::vector< boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_cash_flow.html">CashFlow</a> > > &, const <a class="el" href="class_quant_lib_1_1_interest_rate.html">InterestRate</a> &y, <a class="el" href="class_quant_lib_1_1_date.html">Date</a> settlementDate=<a class="el" href="class_quant_lib_1_1_date.html">Date</a>())</td></tr>
<tr><td class="mdescLeft"> </td><td class="mdescRight">Cash-flow convexity. <a href="#0a537cb39484e47843ee6da7e5320754"></a><br></td></tr>
</table>
<hr><h2>Member Function Documentation</h2>
<a class="anchor" name="0787b5a6401d359520d6b74c4250601e"></a><!-- doxytag: member="QuantLib::Cashflows::npv" ref="0787b5a6401d359520d6b74c4250601e" args="(const std::vector< boost::shared_ptr< CashFlow > > &, const Handle< YieldTermStructure > &)" -->
<div class="memitem">
<div class="memproto">
<table class="memname">
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<td class="memname">static <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> npv </td>
<td>(</td>
<td class="paramtype">const std::vector< boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_cash_flow.html">CashFlow</a> > > & </td>
<td class="paramname">, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a>< <a class="el" href="class_quant_lib_1_1_yield_term_structure.html">YieldTermStructure</a> > & </td>
<td class="paramname"></td><td> </td>
</tr>
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<td></td>
<td>)</td>
<td></td><td></td><td width="100%"><code> [static]</code></td>
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<div class="memdoc">
<p>
NPV of the cash flows.
<p>
The NPV is the sum of the cash flows, each discounted according to the given term structure.
</div>
</div><p>
<a class="anchor" name="cb7212d4823e87c8065e3815a1700c45"></a><!-- doxytag: member="QuantLib::Cashflows::npv" ref="cb7212d4823e87c8065e3815a1700c45" args="(const std::vector< boost::shared_ptr< CashFlow > > &, const InterestRate &, Date settlementDate=Date())" -->
<div class="memitem">
<div class="memproto">
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<td class="memname">static <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> npv </td>
<td>(</td>
<td class="paramtype">const std::vector< boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_cash_flow.html">CashFlow</a> > > & </td>
<td class="paramname">, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_interest_rate.html">InterestRate</a> & </td>
<td class="paramname">, </td>
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<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="class_quant_lib_1_1_date.html">Date</a> </td>
<td class="paramname"> <em>settlementDate</em> = <code><a class="el" href="class_quant_lib_1_1_date.html">Date</a>()</code></td><td> </td>
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<td></td>
<td>)</td>
<td></td><td></td><td width="100%"><code> [static]</code></td>
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<div class="memdoc">
<p>
NPV of the cash flows.
<p>
The NPV is the sum of the cash flows, each discounted according to the given constant interest rate. The result is affected by the choice of the interest-rate compounding and the relative frequency and day counter.
</div>
</div><p>
<a class="anchor" name="9275953ec871b533c6f9dbd28028f4d8"></a><!-- doxytag: member="QuantLib::Cashflows::bps" ref="9275953ec871b533c6f9dbd28028f4d8" args="(const std::vector< boost::shared_ptr< CashFlow > > &, const Handle< YieldTermStructure > &)" -->
<div class="memitem">
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<td class="memname">static <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> bps </td>
<td>(</td>
<td class="paramtype">const std::vector< boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_cash_flow.html">CashFlow</a> > > & </td>
<td class="paramname">, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_handle.html">Handle</a>< <a class="el" href="class_quant_lib_1_1_yield_term_structure.html">YieldTermStructure</a> > & </td>
<td class="paramname"></td><td> </td>
</tr>
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<td></td>
<td>)</td>
<td></td><td></td><td width="100%"><code> [static]</code></td>
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<div class="memdoc">
<p>
Basis-point sensitivity of the cash flows.
<p>
The result is the change in NPV due to a uniform 1-basis-point change in the rate paid by the cash flows. The change for each coupon is discounted according to the given term structure.
</div>
</div><p>
<a class="anchor" name="339005671cfd4aa3d655c5a973776ef3"></a><!-- doxytag: member="QuantLib::Cashflows::bps" ref="339005671cfd4aa3d655c5a973776ef3" args="(const std::vector< boost::shared_ptr< CashFlow > > &, const InterestRate &, Date settlementDate=Date())" -->
<div class="memitem">
<div class="memproto">
<table class="memname">
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<td class="memname">static <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> bps </td>
<td>(</td>
<td class="paramtype">const std::vector< boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_cash_flow.html">CashFlow</a> > > & </td>
<td class="paramname">, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_interest_rate.html">InterestRate</a> & </td>
<td class="paramname">, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="class_quant_lib_1_1_date.html">Date</a> </td>
<td class="paramname"> <em>settlementDate</em> = <code><a class="el" href="class_quant_lib_1_1_date.html">Date</a>()</code></td><td> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td><td width="100%"><code> [static]</code></td>
</tr>
</table>
</div>
<div class="memdoc">
<p>
Basis-point sensitivity of the cash flows.
<p>
The result is the change in NPV due to a uniform 1-basis-point change in the rate paid by the cash flows. The change for each coupon is discounted according to the given constant interest rate. The result is affected by the choice of the interest-rate compounding and the relative frequency and day counter.
</div>
</div><p>
<a class="anchor" name="ab6aff01e22a5a1d97ccde47a65a882f"></a><!-- doxytag: member="QuantLib::Cashflows::irr" ref="ab6aff01e22a5a1d97ccde47a65a882f" args="(const std::vector< boost::shared_ptr< CashFlow > > &, Real marketPrice, const DayCounter &dayCounter, Compounding compounding, Frequency frequency=NoFrequency, Date settlementDate=Date(), Real tolerance=1.0e-10, Size maxIterations=10000, Rate guess=0.05)" -->
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<td class="memname">static <a class="el" href="group__types.html#gede435af51236692b1107d7639581d39">Rate</a> irr </td>
<td>(</td>
<td class="paramtype">const std::vector< boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_cash_flow.html">CashFlow</a> > > & </td>
<td class="paramname">, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>marketPrice</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_day_counter.html">DayCounter</a> & </td>
<td class="paramname"> <em>dayCounter</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">Compounding </td>
<td class="paramname"> <em>compounding</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__datetime.html#g6d41db8ba0ea90d22df35889df452ada">Frequency</a> </td>
<td class="paramname"> <em>frequency</em> = <code>NoFrequency</code>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="class_quant_lib_1_1_date.html">Date</a> </td>
<td class="paramname"> <em>settlementDate</em> = <code><a class="el" href="class_quant_lib_1_1_date.html">Date</a>()</code>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> </td>
<td class="paramname"> <em>tolerance</em> = <code>1.0e-10</code>, </td>
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<td class="paramtype">Size </td>
<td class="paramname"> <em>maxIterations</em> = <code>10000</code>, </td>
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<td class="paramtype"><a class="el" href="group__types.html#gede435af51236692b1107d7639581d39">Rate</a> </td>
<td class="paramname"> <em>guess</em> = <code>0.05</code></td><td> </td>
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<p>
Internal rate of return.
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The IRR is the interest rate at which the NPV of the cash flows equals the given market price. The function verifies the theoretical existance of an IRR and numerically establishes the IRR to the desired precision.
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<a class="anchor" name="4758e38bc3be6c9b70d36f8b6ca5dbdc"></a><!-- doxytag: member="QuantLib::Cashflows::duration" ref="4758e38bc3be6c9b70d36f8b6ca5dbdc" args="(const std::vector< boost::shared_ptr< CashFlow > > &, const InterestRate &y, Duration::Type type=Duration::Modified, Date settlementDate=Date())" -->
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<td class="memname">static <a class="el" href="group__types.html#g14fb8fca43a68f4168654e1f9f7e22f7">Time</a> duration </td>
<td>(</td>
<td class="paramtype">const std::vector< boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_cash_flow.html">CashFlow</a> > > & </td>
<td class="paramname">, </td>
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<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_interest_rate.html">InterestRate</a> & </td>
<td class="paramname"> <em>y</em>, </td>
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<td class="paramtype">Duration::Type </td>
<td class="paramname"> <em>type</em> = <code>Duration::Modified</code>, </td>
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<td class="paramtype"><a class="el" href="class_quant_lib_1_1_date.html">Date</a> </td>
<td class="paramname"> <em>settlementDate</em> = <code><a class="el" href="class_quant_lib_1_1_date.html">Date</a>()</code></td><td> </td>
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<p>
Cash-flow duration.
<p>
The simple duration of a string of cash flows is defined as <p class="formulaDsp">
<img class="formulaDsp" alt="\[ D_{\mathrm{simple}} = \frac{\sum t_i c_i B(t_i)}{\sum c_i B(t_i)} \]" src="form_45.png">
<p>
where <img class="formulaInl" alt="$ c_i $" src="form_46.png"> is the amount of the <img class="formulaInl" alt="$ i $" src="form_47.png">-th cash flow, <img class="formulaInl" alt="$ t_i $" src="form_48.png"> is its payment time, and <img class="formulaInl" alt="$ B(t_i) $" src="form_49.png"> is the corresponding discount according to the passed yield.<p>
The modified duration is defined as <p class="formulaDsp">
<img class="formulaDsp" alt="\[ D_{\mathrm{modified}} = -\frac{1}{P} \frac{\partial P}{\partial y} \]" src="form_50.png">
<p>
where <img class="formulaInl" alt="$ P $" src="form_51.png"> is the present value of the cash flows according to the given IRR <img class="formulaInl" alt="$ y $" src="form_13.png">.<p>
The Macaulay duration is defined for a compounded IRR as <p class="formulaDsp">
<img class="formulaDsp" alt="\[ D_{\mathrm{Macaulay}} = \left( 1 + \frac{y}{N} \right) D_{\mathrm{modified}} \]" src="form_52.png">
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where <img class="formulaInl" alt="$ y $" src="form_13.png"> is the IRR and <img class="formulaInl" alt="$ N $" src="form_36.png"> is the number of cash flows per year.
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<a class="anchor" name="0a537cb39484e47843ee6da7e5320754"></a><!-- doxytag: member="QuantLib::Cashflows::convexity" ref="0a537cb39484e47843ee6da7e5320754" args="(const std::vector< boost::shared_ptr< CashFlow > > &, const InterestRate &y, Date settlementDate=Date())" -->
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<td class="memname">static <a class="el" href="group__types.html#g4bdf4bfe76b9ffa6fa64c47d8bfa0c78">Real</a> convexity </td>
<td>(</td>
<td class="paramtype">const std::vector< boost::shared_ptr< <a class="el" href="class_quant_lib_1_1_cash_flow.html">CashFlow</a> > > & </td>
<td class="paramname">, </td>
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<td class="paramtype">const <a class="el" href="class_quant_lib_1_1_interest_rate.html">InterestRate</a> & </td>
<td class="paramname"> <em>y</em>, </td>
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<td class="paramtype"><a class="el" href="class_quant_lib_1_1_date.html">Date</a> </td>
<td class="paramname"> <em>settlementDate</em> = <code><a class="el" href="class_quant_lib_1_1_date.html">Date</a>()</code></td><td> </td>
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<p>
Cash-flow convexity.
<p>
The convexity of a string of cash flows is defined as <p class="formulaDsp">
<img class="formulaDsp" alt="\[ C = \frac{1}{P} \frac{\partial^2 P}{\partial y^2} \]" src="form_53.png">
<p>
where <img class="formulaInl" alt="$ P $" src="form_51.png"> is the present value of the cash flows according to the given IRR <img class="formulaInl" alt="$ y $" src="form_13.png">.
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